A hybrid difference scheme for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

A singularly perturbed convection diffusion problem with a discontinuous convection coefficient is considered. Due to the discontinuity an interior layer appears in the solution. The problem is solved using a hybrid difference scheme on a Shishkin mesh. We prove that the method is almost second-order convergent in the maximum norm, independently of the diffusion parameter. Numerical experiments support these theoretical results and indicate that the estimates are sharp.